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math.PR2026
Free multiplicative convolution with an arbitrary measure on the real line
Octavio Arizmendi, Takahiro Hasebe, Yu Kitagawa
We develop analytic tools for studying the free multiplicative convolution of any measure on the real line and any measure on the nonnegative real line. More precisely, we construc…
math.PR2024
Central limit theorem for crossings in randomly embedded graphs
Santiago Arenas-Velilla, Octavio Arizmendi, J. E. Paguyo
We consider the number of crossings in a random embedding of a graph, , with vertices in convex position. We give explicit formulas for the mean and variance of the number of cr…
math.PR2024
New combinatorial identity for the set of partitions and limit theorems in finite free probability theory
Octavio Arizmendi, Katsunori Fujie, Yuki Ueda
We provide a refined combinatorial identity for the set of partitions of , which plays an important role in investigating several limit theorems related to finite f…